EXISTENCE OF INFINITELY MANY SOLUTIONS FOR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT

作     者：傅红卓 沈尧天 Fu Hongzhuo Shen YaotianDepartment of Mathematics, South China University of Technology, Guangzhou 510640, China Department of Mathematics, University of Science and Technology of China, Hefei 230026, China

作者机构：Department of Mathematics South China University of Technology Guangzhou 510640 China Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics South China University of Technology Guangzhou 510640 Chinahis paper is concerned with the following nonlinear Dirichlet problem:where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u Ωis a bounded domain in Rn (n > 3) 1 < p < n p = -pn/n-p is the critical exponent for the Sobolev imbedding λ> 0 and f(x u) satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p = 2 or f(xu) = |u|q-2u where 1 < q < p are generalized. 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2004年第24卷第3期

页      面：395-402页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by NSFC(10171032) NSF of Guangdong Proviance (011606) 

主　　题：critical Sobolev exponent concentration compactness principle genus infinitely many solutions 

摘      要：This paper is concerned with the following nonlinear Dirichlet problem: where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u, Ω is a bounded domain in Rn (n 3), 1 0 and f(x, u) satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p = 2 or f(x,u) = |u|q-2u, where 1 q p, are generalized.